The present invention relates to the field of seismic data processing. In particular, the present invention relates to methods of attenuating noise in three-dimensional seismic data.
A seismc signal which consists of only linear events has an f-x domain representation which is predictable in x for each frequency f. A generalization of this results is easy to show: the f-xy domain representation of a 3-D (timexe2x80x94spacexe2x80x94space) seismic signal, which consists of only planar events, is perfectly predictable in the xy-plane for each frequency f. The significance of this result is that, some problems such as reducing noise in a 3-D volume can be reduced to a set of 2-D problems in the xy-plane, which are easier to solve. For each frequency f, the noise is attenuated regardless of the data at other frequencies. For this purpose, what is needed is an algorithim which separates 2-D predictable data from additive noise. F-xy prediction (i.e. f-xy decon) is conventionally used for this purpose. For example, see the following references: M. Chase, xe2x80x9cRandom noise reduction by FXY prediction filtering,xe2x80x9d EAGE Conf. Exp. Abs., Paris, pp. 164-165, 1992; M. Chase, xe2x80x9cRandom noise reduction by 3-D spatial prediction filtering,xe2x80x9d SEG Ann. Mtg. Exp. Abs., New Orleans, pp. 1152-1153, 1992; and N. Gulunay, V. Sudhakar, C. Gerrard, and D. Monk, xe2x80x9cPrediction filtering for 3-K poststack data,xe2x80x9d SEG Ann. Mtg. Exp. Abs., Washington, D.C., pp. 1183-1186, 1993.
Unfortunately, the f-xy prediction methods suffer from model inconsistency problems. The model inconsistency in the f-xy prediction method adversely affects signal preservation and noise attenuation when applied to seismic data. This disadvantage is similar to the model inconsistency problem in the 1-D counterpart to the f-xy prediction method, namely the f-x prediction algorithm. For an example of f-x prediction, see: Canales, xe2x80x9cRandom noise reduction,xe2x80x9d 54th SEG Ann Mtg. Exp. Abs., Atlanta, pp. 525-527, 1984; and N. Gulunay, xe2x80x9cFXDECON and complex wiener prediction filter,xe2x80x9d SEG Ann, Mtg. Exp. Abs., Houston, pp. 279-281, 1986.
The f-x projection algorithm is described in for example, the following references: R. Soubaras, xe2x80x9cSignal-preserving random noise attenuation by the f-x projection,xe2x80x9d SEG Ann Mtg. Exp. Abs., Los Angeles, pp. 1576-1579, 1994; R Soubaras, xe2x80x9cDeterministic and statistical projection filtering for signal-presrving noise attenuation,xe2x80x9d EAGE Conf. Exp. Abs., Glasgow. A051, 1995; R. Soubaras, xe2x80x9cPrestack random and impulsive noise attenuadon by f-x projection filtering,xe2x80x9d SEG Ann. Mtg. Exp. Abs., Houston, pp. 711-714, 1995; R. Soubaras, xe2x80x9cthe necessary and sufficient condition for lossless-sampling,xe2x80x9d EAGE Conference and Technical Exhibition, Geneva, 1997; and U.S. Pat. No. 5,771,203. However, the f-x projection algorithm has the limitation in that it is only applicable to 2-D data.
Thus, it is an object of the invention to provide a noise attenuation algorithm that does not suffer from the same problems and limitations of the prior art. In particular, it is an object of the invention to provide an algorithm for attenuating noise in three-dimensional seismic data which does not suffer from model inconsistency problems known in conventional methods.
According to the invention, a method of attenuating noise in three dimensional seismic data is provided. The method includes receiving seismic data representing data gathered in at least two spatial dimensions and a time dimension. The seismic data includes both a noise component and a seismic signal component. The latter of which represents signals originating from at least one seismic disturbance. Values are computed for use in a projection filter, which is used to estimate the noise component of the seismic data. Spectral factorization is then performed in at least two dimensions to obtain additional two-dimensional values for use in the projection filter. The noise component in said received seismic data is estimated by using the projection filter which includes at least some of the additional two-dimensional values. The estimated noise component is then subtracted from the received data to obtain attenuated seismic data having a decreased noise component.
According to a preferred embodiment of the invention, the method also includes causing at least one seismic disturbance, recording raw data from a plurality of sensors distributed in at least two spatial dimensions; and then processing the recorded raw data to form said seismic data.
According to a preferred embodiment of the invention, the method also includes performing a Fourier Transform with respect to time of the seismic data to obtain frequency domain seismic data, selecting a single frequency from said frequency domain seismic data; and repeating for each desired frequency said steps of computing values, performing spectral factorization, estimating the noise component, and subtracting the estimated noise.
According to a preferred embodiment of the invention, the method also includes creating an initial estimate for an initial spectral factor sequence of values to be used in the projection filter, applying an all-pole filter based on the inverse of the square of the initial spectral factor sequence of values to obtain an intermediate sequence of values; computing an autocorrelation of the intermediate sequence of values; and finding coefficients for use in the projection filter by solving normal equations using the autocorrelation of the intermediate sequence of values.
According to a preferred embodiment of the invention, the spectral factorization is performed using a helical coordinate transform on the autocorrelation of the intermediate sequence of values to obtain a one-dimensional sequence, and the factorization is preformed on the one-dimensional sequence to obtain a one-dimensional factor, which is mapped into two-dimensions using an inverse of the helical coordinate transform to obtain a two-dimensional factor which represents some of said additional two-dimensional values.
According to a preferred embodiment of the invention, the noise component of the seismic data is primarily random noise, and the projection filter estimates primarily random noise.
According to another preferred embodiment of the invention, the noise component of the seismic data is primarily coherent noise, and the projection filter estimates primarily coherent noise.